Question

A battery-operated car uses a 12.0-V system. Find the charge the batteries must be able to move in order to accelerate the 956kg car from rest to 158m/s.

Answer 1

1.99 x 10⁶C

Step-by-step explanation:

The electrical energy (
`E_(E)`) stored in the battery will give the car some kinetic energy (
`E_(K)`) which will cause the car to move from rest to some other point.

i.e

`E_(E)` =
`E_(K)` ------------------(i)

But;

`E_(E)` =
`(1)/(2)` x Q x V; -------------------(ii)

Where;

Q = charge on the battery

V = potential difference or voltage of the battery = 12.0V

Also

`E_(K)` = (
`(1)/(2)` x m x v²) - (
`(1)/(2)` x m x u²) -----------------(iii)

Where;

m = mass of the car = 956kg

v = final velocity of the car = 158m/s

u = initial velocity of the car = 0 [since the car starts from rest]

Substitute equations (ii) and (iii) into equation (i) as follows;

`(1)/(2)` x Q x V = (
`(1)/(2)` x m x v²) - (
`(1)/(2)` x m x u²) -----------------(iv)

Substitute all necessary values into equation (iv) as follows;

`(1)/(2)` x Q x 12.0 = (
`(1)/(2)` x 956 x 158²) - (
`(1)/(2)` x 956 x 0²)

`(1)/(2)` x Q x 12.0 = (
`(1)/(2)` x 956 x 158²) - (0)

`(1)/(2)` x Q x 12.0 = (
`(1)/(2)` x 956 x 158²)

`(1)/(2)` x Q x 12.0 = 11932792

6Q = 11932792

Solve for Q;

Q = 11932792 / 6

Q = 1988798.67 C

Q = 1.99 x 10⁶C

Therefore, the amount of charge the batteries must have is 1.99 x 10⁶C