Question

A cyclist accelerates from a velocity of 10 miles/hour east until reaching a velocity of 20 miles/hour east in 5 seconds. What was the cyclist's acceleration?

Answer 1

`a = 0.894\ m/s^2`

Step-by-step explanation:

Motion with Constant Acceleration

A body moves with constant acceleration when the speed changes uniformly in time. The equation used to find the final speed vf is

`v_f=v_o+at`

Where vo is the initial speed, a is the acceleration, and t is the time.

The cyclist has an initial speed of vo=10 miles/hour and ends up at vf=20 miles/hour in t=5 seconds.

Both speeds are given in miles/hour and we must convert it to m/s:

1 mile/hour = 0.44704 m/s

10 mile/hour = 4.47 m/s

20 mile/hour = 8.94 m/s

The acceleration is calculated by solving for a:

`\displaystyle a=(v_f-v_o)/(t)`

`\displaystyle a=(8.94-4.47)/(5)`

`a = 0.894\ m/s^2`