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.

1.99 x 10⁶C

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

i.e

=                 ------------------(i)

But;

=   x Q x V;            -------------------(ii)

Where;

Q = charge on the battery

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

Also

= ( x m x v²) - ( 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;

x Q x V = ( x m x v²) - ( x m x u²)       -----------------(iv)

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

x Q x 12.0 = ( x 956 x 158²) - ( x 956 x 0²)

x Q x 12.0 = ( x 956 x 158²) - (0)

x Q x 12.0 = ( x 956 x 158²)

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

it should be -8.6 cm hope this out