Constant acceleration formulae

Use the formula

v = u + at

to find the final velocity, when:

• the initial velocity is 8 m/s

• the acceleration is 6.5 m/s²

• the time is 14 seconds.

Use the formula

to find the value of q when p = 39 and r = 6.

You may use these kinematics formulae to answer this question.

v = u + at

where a is the constant acceleration, u is the initial velocity, v is the final velocity, s is the displacement and t is the time taken.

A particle has an initial velocity of 2 m/s. After 6 seconds the particle has a velocity of 11 m/s. The particle had constant acceleration.

Work out the distance the particle has travelled in the 6 seconds.

You may use these kinematics formulae to answer these questions.

v = u + at

v² = u² + 2as

A moving particle accelerates at 2 m/s² for 8 seconds. The particle’s final velocity after the 8 seconds is 21 m/s.

Show that the velocity of the particle at the start of the 8 seconds is 5 m/s.

Work out the distance travelled by the particle during the 8 seconds.

Use the formula

v² = u² + 2as

to find the final velocity when

• the initial velocity is 6 m/s

• the acceleration is 4 m/s²

• the distance travelled is 8 m.

The following kinematics formulas may be used in this question.

v = u + at

v² = u² + 2as

A particle has an initial velocity of 0 m/s. The particle accelerates uniformly at 3 m/s² for 4 seconds.

Find the distance travelled by the particle in the 4 seconds.

Show that the formula v = u + at can be rearranged to a =

Use the formula

to find the acceleration, am/s², when a particle takes 4 seconds to increase from an initial velocity of 3 m/s to a final velocity of 9 m/s.

Rearrange this formula to make u the subject.

A rocket accelerates at 90 m / s² and travels 270 km. The rocket’s final velocity is 8000 m / s.

Using part (a), or otherwise, calculate the rocket’s initial velocity in m / s.

Rearrange this formula to make d the subject.

f = 5 d + 4

Use the formula

v = u + at

to find the final velocity, when

• the initial velocity is 5 m/s

• the acceleration is 7.5 m/s²

• the time is 6 seconds.

You may use these kinematics formulae to answer this question.

v = u + at

A particle has an initial velocity of 3 m/s. After 20 seconds the particle has a velocity of 11 m/s.

Work out the distance the particle has travelled after 20 seconds.

A car accelerates at 4.06 m/s² for 10.1 seconds from an initial velocity of 2.93 m/s.

Harper rounds each value to 1 significant figure. Harper uses the rounded values and the formula

to estimate the distance travelled in the 10.1 seconds. Harper’s answer is 430 metres.

Using Harper’s method, show that their answer is wrong.

Rearrange this formula to make t the subject.

The following kinematics formulas may be used in this question.

v = u + at

v² = u² + 2as

The initial velocity of a particle is 20 m/s. The acceleration of the particle is -8 m/s². After t seconds, the particle has travelled 25 m.

Show that 4t² - 20t + 25 = 0.

Solve 4t² - 20t + 25 = 0.

Show that the particle is stationary when it has travelled 25 m.

A train is travelling with a velocity of 15 m / s. It then accelerates at 0.5 m / s² for 6 seconds.

Use the formula v = u + at to calculate the velocity of the train after the 6 seconds.

Rearrange the formula v = u + at to make a the subject.

A leopard is running with a velocity of 3 m/s. It then accelerates at 2 m/s² for 4 seconds.

Use the formula

v = u + at

to work out the final velocity of the leopard.

Find the value of 3 a + 2 b when a = 16 and b = 7.

Use the formula

v = u + at

to find the final velocity, when

• the initial velocity is 2 m/s

• the acceleration is 1.5 m/s²

• the time is 6 seconds.

Make d the subject of this formula.

c = 7 d

Find the value of s when u = 12, a = 10 and t = 4.