# Worksheet: Linear Motion with Definite Integrals

Q1:

A particle is moving in a straight line such that its speed at time seconds is given by Given that its initial position , find its position when .

Q2:

A particle started moving in a straight line from the origin such that its acceleration at time seconds is given by Given that its initial velocity was 14 m/s, determine its velocity and its displacement when .

• A ,
• B ,
• C ,
• D ,

Q3:

The acceleration of a particle moving in a straight line, at time seconds, is given by When , the particle moves with uniform velocity . Determine the velocity and the distance, , covered by the particle in the first 23 s of motion.

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

A body started moving along the -axis from the origin at an initial speed of 10 m/s. When it was meters away from the origin and moving at m/s, its acceleration was m/s2 in the direction of increasing . Determine when .

• A m
• B m
• C m
• D m
• E m

Q5:

A particle started moving in a straight line from point towards point . Its velocity after seconds is given by After 2 seconds, another particle started moving in a straight line from point towards point . This particle was accelerating at 0.9 m/s2. The two particles collided 6 seconds after the first particle started moving. Find the distance .

Q6:

A particle, starting from rest, began moving in a straight line. Its acceleration , measured in metres per second, and the distance from its starting point, measured in metres, satisfy the following equation . Find the speed of the particle when .

• A
• B
• C
• D

Q7:

A body moves in a straight line. At time seconds, its acceleration is given by Given that the initial displacement of the body is 9 m, and when , its velocity is 27 m/s, what is its displacement when ?

Q8:

A particle is moving in a straight line such that its velocity after seconds is given by Find the distance covered during the time interval between and .

Q9:

A particle is moving in a straight line such that its acceleration, meters per second squared, and displacement, meters, satisfy the equation . Given that the particle's velocity was 12 m/s when its displacement was 0 m, find an expression for in terms of , and determine the speed that the particle approaches as its displacement increases.

• A ,
• B ,
• C ,
• D ,

Q10:

A particle is moving in a straight line such that its velocity at time seconds is given by Given that its initial position , find an expression for its position at time seconds.

• A m
• B m
• C m
• D m

Q11:

The figure shows a velocity-time graph for a particle moving in a straight line. Find the magnitude of the displacement of the particle.

Q12:

The diagram below shows the acceleration of a particle which was initially at rest. What was its velocity at ?

Q13:

A particle started moving in a straight line. Its acceleration at time seconds is given by Find the maximum velocity of the particle and the distance it travelled before it attained this velocity.

• A ,
• B ,
• C ,
• D ,

Q14:

A particle moves in a straight line. At time seconds, its velocity, in meters per second, is given by What is its displacement in the interval ?

Q15:

A particle started moving in a straight line such that its acceleration, measured in meters per second, and its displacement from a fixed point, measured in meters, satisfy the following equation: . Given that its initial displacement from the fixed point was 9 meters and its initial velocity was 5 m/s, determine its velocity when .

• A 22 m/s
• B 9 m/s
• C 21 m/s
• D 4 m/s

Q16:

A particle moves along the axis. It is initially at rest at the origin. At time seconds, the particleβs acceleration is given by How long does it take for the particle to return to the origin?

• A s
• B s
• C s
• D s

Q17:

A particle is moving in a straight line such that its acceleration at time seconds is given by Given that its initial velocity is m/s and its initial position from a fixed point is m, determine its position when seconds.

• A m
• B m
• C m
• D m

Q18:

A particle started moving from rest along the -axis from a point at . Its acceleration at time seconds is given by Express its velocity and its displacement after time seconds.

• A ,
• B ,
• C ,
• D ,

Q19:

A particle started moving from a fixed point in a straight line such that its acceleration , measured in metres per second squared, and its position , measured in metres, satisfy the following equation: . Given that the initial velocity of the particle was 2 m/s, find an expression for in terms of .

• A
• B
• C
• D

Q20:

A particle starts from rest and moves in a straight line. At time seconds, its velocity is given by How long does it take for the particle to return to its starting point?

Q21:

The acceleration-time graph of a particle which was initially at rest is shown below. What was its velocity at ?

Q22:

A particle is moving in a straight line such that its velocity at time seconds is given by Given that when seconds its position from a fixed point is , find an expression for in terms of .

• A
• B
• C
• D

Q23:

The given acceleration-time graph represents the motion of a particle. Given that the particle moved in a straight line and was at rest at time , find the velocity of the particle at .

Q24:

A particle started moving on the -axis from the origin at an initial velocity . At time seconds, the particleβs acceleration is given by Given that after 6 seconds, the particleβs displacement was 75 m in the right from point , Determine . If the body passed by once again, determine its velocity at this moment.

• A ,
• B ,
• C ,
• D ,
• E ,

Q25:

Two bodies, initially at rest at the same point, start to move in the same direction along the same straight line. At time seconds , their velocities are given by and . Determine the time taken for the two bodies to be 2β744 cm apart.