## Applications of SUVAT

SUVAT may be used whenever motion is broken up into periods of motion where the acceleration is constant. For example, if a heavy ball is dropped from a height and hits soft ground, decelerating rapidly and coming to rest, we can apply SUVAT to the period of motion when the ball is falling before it hits the ground, and separately to the period of motion after the ball hits the ground and is decelerating rapidly. During both periods of motion we assume the acceleration is constant, otherwise we cannot use the SUVAT equations, and we can take the final velocity of the initial period of motion, when the ball is falling, to be equal to the initial velocity for the final period of motion. For ease of reference the SUVAT equations are:

(1)

(2)

(3)

(4)

(5)

To develop the example above, suppose the ball is dropped from a height of 10m, and when it hits the ground, penetrates to a depth of 3cm.

a)Find the speed of ball when it hits the ground

b)Find the time after the ball hits the ground to come to rest and the average deceleration.

a) s=-10

u=0

v=?

a=-9.8

t=?

We take the negative square root because the ball is moving down.

b) s=-0.03

u=-14

v=0

a=?

t=?