HARD
AS and A Level
IMPORTANT
Earn 100

A crane lifts a block from ground level at a constant speed of v m s-1. After 5 s the block slips from its shackles and decelerates at 10 m s-2. It reaches a maximum height of 6 m. Find the value of v.

Important Questions on Velocity and Acceleration

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 12
A car is at rest when it accelerates at 5 m s-2 for 4 s. It then continues at a constant velocity. At the instant the car starts moving, a truck passes it, moving at a constant speed of 22 m s-1. After 10 s the truck starts slowing at 1 m s-2 until coming to rest.
Show that the velocities are equal after 12 s and, hence, find the maximum distance between the car and the truck.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 12
A car is at rest when it accelerates at 5 m s-2 for 4 s. It then continues at a constant velocity. At the instant the car starts moving, a truck passes it, moving at a constant speed of 22 m s-1. After 10 s the truck starts slowing at 1 m s-2 until coming to rest.
Show that the distance covered at a time t s from the start by the car and the truck, for t>10, are given by 40+20(t-4) and 220+22(t-10)-12(t-10)2, respectively. Hence, find the time at which the car passes the truck.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 13

Two cyclists are having a race along a straight road. Bradley starts 50 m ahead of Chris. Bradley starts from rest, accelerates to 15 m s-1 in 10 s and remains at this speed for 40 s before decelerating at 0.5 m s-2. Chris starts 5 s later than Bradley. He starts from rest, accelerates to 16 m s-1 in 8 s and maintains this speed.

Show that Bradley is still ahead when he starts to slow down, and find how far ahead he is.

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 13

Two cyclists are having a race along a straight road. Bradley starts 50 m ahead of Chris. Bradley starts from rest, accelerates to 15 m s-1 in 10 s and remains at this speed for 40 s before decelerating at 0.5 m s-2. Chris starts 5 s later than Bradley. He starts from rest, accelerates to 16 m s-1 in 8 s and maintains this speed.

Find the amount of time Bradley has been cycling when he is overtaken by Chris.

MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 14

A driver travelling at 26 m s-1 sees a red traffic light ahead and starts to slow at 3 m s-2 by removing her foot from the accelerator pedal. A little later she brakes at 5 m s-2 and comes to rest at the lights after 6 s.

Sketch the velocity-time graph of the motion.

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 14

A driver travelling at 26 m s-1 sees a red traffic light ahead and starts to slow at 3 m s-2 by removing her foot from the accelerator pedal. A little later she brakes at 5 m s-2 and comes to rest at the lights after 6 s.

Find the equations of the two sections of the graph.

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 14

A driver travelling at 26 m s-1 sees a red traffic light ahead and starts to slow at 3 m s-2 by removing her foot from the accelerator pedal. A little later she brakes at 5 m s-2 and comes to rest at the lights after 6 s.

Hence, find the time when the driver needs to start braking.

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 15

A car accelerates from rest to a speed v m s-1 at a constant acceleration. It then immediately decelerates at a constant deceleration until coming back to rest t s after starting the motion.

Show that the distance travelled is independent of the values of the acceleration and deceleration.