Worksheet: Rectilinear Motion and Integration
In this worksheet, we will practice applying integrals to solve problems involving motion in a straight line.
A particle moves along the positive -axis, starting at . Its acceleration varies directly with , where is the time in seconds. At , the particle’s displacement is 12 m, and its velocity is 14 m/s. Express the particle’s displacement, , and its velocity, , in terms of .
If is the velocity of a particle in motion, in kilometers per hour, what is the unit of ?
- Bhours per kilometer
- Ckilometers per hour
A sky diver jumped out of a plane. His terminal velocity was 55 m/s. Given that the air resistance is directly proportional to the velocity, how long did it take for his speed to reach 54 m/s? Round your answer to three significant figures. Take .
The velocity function, in meters per second, for a particle moving along a line is . Determine the particle’s displacement during the time interval .
- A m
- B m
- C33 m
- D m
- E m
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 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
A particle started moving in a straight line from point toward point . Its velocity after seconds is given by . After 2 seconds, another particle started moving from rest in a straight line from point toward 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 .
A particle, starting from rest, began moving in a straight line. Its acceleration , measured in meters per second squared, and the distance from its starting point, measured in meters, satisfy the equation . Find the speed of the particle when .
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 .
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.
The figure shows a velocity-time graph for a particle moving in a straight line. Find the magnitude of the displacement of the particle.
The diagram below shows the acceleration of a particle which was initially at rest. What was its velocity at ?