Worksheet: Acceleration over Distance and Time

In this worksheet, we will practice calculating acceleration using an object's initial velocity, its displacement, and its acceleration time using the formula s = ut + ½at².

Q1:

A car that was initially moving at a steady speed travels a distance of 15 m while accelerating in a straight line for 10 seconds at 2.5 m/s2 in the opposite direction to its original velocity. What was the car’s initial speed?

Q2:

An object has an initial velocity of 12 m/s. The object accelerates at 2.5 m/s2 in the same direction of its velocity for a time of 1.5 s. What is the displacement of the object during this time? Answer to one decimal place.

Q3:

An object has an initial velocity of 10 m/s. The object accelerates at 1.5 m/s2 in the opposite direction to its velocity for a time of 2.5 s. What is the net displacement of the object in the direction of its initial velocity during this time? Answer to one decimal place.

Q4:

The graph shows the change in velocity of an object with time. The object reverses its direction of motion twice during the 60 seconds for which it moves. The initial direction of motion is toward the north.

After 60 s of motion, is the object moving north or south?

  • AThe object is not moving.
  • BThe object is moving north.
  • CThe object is moving south.

After 60 s of motion, what is the distance of the object from its starting position?

Q5:

A bicycle has an initial velocity of 10 m/s and it accelerates for 7.5 seconds. After this time, the bicycle is at a distance of 55 m from the point at which it began accelerating. What was the bicycle’s rate of acceleration? Answer to two decimal places.

  • A 2 . 6 7 m/s2
  • B 0 . 3 6 m/s2
  • C 0 . 7 1 m/s2
  • D 5 . 3 0 m/s2
  • E 4.62 m/s2

Q6:

An object has an initial velocity of 32 m/s. The object accelerates at 12 m/s2 in the opposite direction to its velocity for a time of 5.5 s. What is the net displacement of the object in the direction of its initial velocity during this time?

Q7:

The graph shows the change in velocity of an object with time.

What is the object’s velocity at 𝑡 = 0 ?

For how long does the object accelerate?

What is the object’s velocity after it has accelerated?

What is the object’s acceleration?

What is the object’s displacement?

Q8:

The change in an object’s velocity with time is shown in the graph. The object has a velocity 𝑢 at the time 𝑡 and a velocity 𝑣 at the time 𝑡 .

What quantity is equal to the quantity velocity multiplied by the quantity time?

  • ADistance
  • BAcceleration
  • CSpeed
  • DDisplacement

Which of the following is the correct expression for value of the area 𝐵 shown in the graph?

  • A 𝑢 Δ 𝑡
  • B ( 𝑣 𝑢 ) Δ 𝑡
  • C Δ 𝑡 𝑢
  • D 𝑢 Δ 𝑡

Which of the following is the correct expression for value of the area 𝐴 shown in the graph?

  • A 1 2 ( 𝑣 𝑢 ) Δ 𝑡
  • B ( 𝑢 + 𝑣 ) Δ 𝑡
  • C 1 2 ( 𝑢 𝑣 ) Δ 𝑡
  • D 1 2 ( 𝑢 + 𝑣 ) Δ 𝑡
  • E 2 ( 𝑢 + 𝑣 ) Δ 𝑡

Which of the following formulas correctly expresses the relationship between acceleration, displacement, and change in time shown by the graph?

  • A 𝑠 = 𝑢 Δ 𝑡 + 1 2 𝑎 Δ 𝑡
  • B 𝑠 = 1 2 𝑢 Δ 𝑡 + 1 2 𝑎 Δ 𝑡
  • C 𝑠 = 𝑢 Δ 𝑡 + 1 2 𝑎 Δ 𝑡
  • D 𝑠 = 1 2 𝑢 Δ 𝑡 + 𝑎 Δ 𝑡

Q9:

A car is traveling east and passes the point 𝑃 that is 45 m east of a road junction. As the car passes the point 𝑃 , its speed is 30 m/s and the driver applies the brakes, accelerating west at 2.5 m/s2. What distance east of the road junction is the car 10 s after the brakes are applied?

Q10:

A car that was initially moving at a steady speed has a net displacement of 45 m after accelerating in a straight line at 1.5 m/s2 for 15 seconds. What was the car’s initial velocity in the direction of its acceleration?

Q11:

A bicycle has an initial velocity of 12 m/s and it accelerates for 15 s in the direction of its velocity, moving 220 m during that time. What is the bicycle’s rate of acceleration? Answer to two decimal places.

  • A 5.30 m/s2
  • B 1.80 m/s2
  • C 0.18 m/s2
  • D 0.36 m/s2
  • E 3.60 m/s2

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