Why does s = (u + v)t/2 work for constant acceleration?

The average velocity is the mean of u and v because velocity changes at a constant rate.

What is the acceleration of a ball thrown upwards at its highest point?

9.81 m s⁻² downwards; the velocity is zero but the acceleration is unchanged.

How do you find the time for a ball thrown up to return to its starting height?

Set s = 0 in s = ut + ½at² to get t = 2u/g, or double the time to the top.

What should you do if the acceleration changes during a journey?

Split the journey into stages with constant acceleration and apply the equations to each stage, using the final velocity of one stage as the initial velocity of the next.

Equations of uniformly accelerated motionEdexcel International A Level Physics: Flashcards

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Question

What condition must be met to use the suvat equations?

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What condition must be met to use the suvat equations?: The acceleration must be constant, in a straight line.
State the equation linking v, u, a and t.: v = u + at
State the equation for displacement using average velocity.: s = (u + v)t/2
State the equation for displacement that contains u, a and t.: s = ut + ½at²
State the equation that does not contain time.: v² = u² + 2as
Which equation do you use if you are not given or asked for s?: v = u + at
Which variable is missing from s = ut + ½at²?: The final velocity v.
Why does s = (u + v)t/2 work for constant acceleration?: The average velocity is the mean of u and v because velocity changes at a constant rate.
What is the value of v for an object that comes to rest?: Zero.
What is the sign of the acceleration of a braking vehicle if its initial direction is positive?: Negative.
What is the acceleration of a ball thrown upwards at its highest point?: 9.81 m s⁻² downwards; the velocity is zero but the acceleration is unchanged.
How do you find the time for a ball thrown up to return to its starting height?: Set s = 0 in s = ut + ½at² to get t = 2u/g, or double the time to the top.
What should you do if the acceleration changes during a journey?: Split the journey into stages with constant acceleration and apply the equations to each stage, using the final velocity of one stage as the initial velocity of the next.

Exam questions on Equations of uniformly accelerated motion

A car travelling in a straight line on a level road at 24 m s⁻¹ brakes with a constant deceleration and comes to rest after 6.0 s.
Calculate the distance travelled by the car in the first 3.0 s of braking.2 marks
A ball is thrown vertically upwards from a point at ground level with an initial speed of 15 m s⁻¹. Air resistance is negligible and the acceleration of free fall is 9.81 m s⁻².
Calculate the time taken for the ball to return to ground level.2 marks
A driver is travelling at 20 m s⁻¹ along a straight road. When the driver sees an obstacle there is a reaction time of 0.70 s before the brakes are applied, during which the speed stays constant. The car then decelerates uniformly at 6.0 m s⁻² until it stops or hits the obstacle.
Calculate the distance the car travels from the moment the driver sees the obstacle until the car stops.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).