AH 1.1 Kinematic Relationships

Question 1

Derive the kinematic relationship v=u+at

Answer 1

Question 2

Derive the kinematic relationship

s = ut + 1/2 at²

Answer 2

Question 3

Derive the kinematic relationship v² = u² + 2as

Answer 3

Question 4

A body undergoes uniform acceleration.

Write down the general equation for its displacement s with respect to time t.

Answer 4

s = ut + ½ at²

Question 5

The initial velocity of a body is 20 ms^-1 and it’s acceleration is 6 ms^-2.

Write down the particular equation for the displacement of this body.

Answer 5

s = 20t + 3t²

Question 6

A body has diplacement equation s = 20t + 3t²

Using differentiation, find the equation for the velocity of this body.

Show all reasoning.

Answer 6

v = ds/dt

= d/dt (20t + 3t²)

v = 20 + 6t

Question 7

Given the velocity equation for a moving body is v = 20 + 6t, differentiate this velocity equation to confirm that the acceleration is 6 ms^-2. Show all steps of reasoning.

Answer 7

a = dv/dt

= d/dt (20 + 6t)

a = 6 ms^-2

Question 8

The displacement of a firework rocket for the first 3 seconds of its motion is given by the equation

s = 8t³ + 4t²

Find expressions for the velocity and acceleration of the rocket. Show all steps of reasoning.

Answer 8

v = ds/dt

v = 24t² + 8t

a = dv/dt

a = 48t +8

Question 9

The displacement of a firework rocket is given by s = 8t³ +4t²

After 3 seconds find the displacement of the rocket.

Answer 9

s = 252 m

Question 10

The velocity of a firework rocket is given by

v = 24t² + 8t

Find the velocity after 3 seconds.

Answer 10

v = 240 ms^-1

Question 11

The acceleration of a firework rocket is given by the equation a = 48t +8

Findf the acceleration after 3 seconds.

Answer 11

a = 152 ms^-2

Question 12

Give a physical reason for why the displacement, velocity and acceleration equations for a firework rocket after launch only hold for the first 3 seconds.

Answer 12

The firework rocket must have run out of fuel after 3 seconds.

Question 13

The displacement of a firework rocket after launch is given by s = 8t³ +4t²

Give a mathematical reason why this equation only holds for 3 seconds.

Answer 13

The displacement equation suggests that s increases indefinitely!

This is clearly impossible as there is only a finite amount of fuel.