Question

The velocity of a car changes from 10 m/s east to 30 m/s east in 4 seconds. What is the acceleration of the car?

A.
10 m/s2 east
B.
5 m/s2 east
C.
5 m/s2 west
D.
10 m/s2 west

Answer 1

5 m/s² east

Step-by-step explanation:

Acceleration is change in velocity over change in time. It can be expressed mathematically as:

`\displaystyle{\vec a = (\Delta \vec v)/(\Delta t)}\\\\\displaystyle{\vec a = (\vec v_2 - \vec v_1)/(t_2-t_1)}`

Where
`\displaystyle{\vec v_2}` is final velocity,
`\displaystyle{\vec v_1}` is initial velocity,
`\displaystyle{t_2}` is final time and
`\displaystyle{t_1}` is initial time.

Therefore, from the problem, we know that:

• final velocity is 30 m/s east.
• initial velocity is 10 m/s east.
• final time is 4 seconds.
• initial time is 0 second.

Therefore:

`\displaystyle{\vec a = \frac{30 \ \, \sf{m/s} \ \, east- 10 \ \, m/s \ \, east}{4 \ \, \sf{seconds}-0\ \, seconds}}\\\\\displaystyle{\vec a = \frac{20 \ \, \sf{m/s} \ \, east}{4 \ \, \sf{seconds}}}\\\\\displaystyle{\vec a = 5 \ \, \sf{m/s^2} \ \, \sf{east}}`

Therefore, acceleration will be 5 m/s² east.