A motorbike is traveling to the left with a speed of 27.0 m s 27.0 s m 27, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction when the rider slams on the brakes. The bike skids 41.5 m 41.5m41, point, 5, start text, m, end text with constant acceleration before it comes to a stop. What was the acceleration of the motorbike as it came to a stop?

The acceleration of the motorbike as it came to a stop was -8.78 m/s² (NOTE: Negative sign indicates deceleration)  

Explanation:

From the question,

A motorbike is traveling to the left with a speed of 27.0 m/s.

This is the initial speed, that is, initial speed = 27.0 m/s

Also, from the question,

The rider slams on the brakes and the bike skids 41.5 m, that is, the bike covers a distance of 41.5 m after the rider slams on the brakes.

Distance = 41.5 m

To determine the acceleration of the motorbike as it came to a stop,

Since, the bike came to a stop, then, the final speed is 0 m/s

From one of the equations of motion for linear motion

v² = u² + 2as

Where v is the final speed (velocity)

u is the initial speed (velocity)

a is the acceleration

and s is the distance

From the question

v = 0 m/s

u = 27.0 m/s

s = 41.5 m

Putting these into the equation

v² = u² + 2as

0² = 27.0² + (2×a×41.5)

0 = 729.0 + 83a

83a = -729.0

a = -729.0 / 83

a = -8.78 m/s² (NOTE: Negative sign indicates deceleration)  

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