1.99 x 10⁶C
<h2>Explanation:</h2>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)
<em>But;</em>
=
x Q x V; -------------------(ii)
Where;
Q = charge on the battery
V = potential difference or voltage of the battery = 12.0V
<em>Also</em>
= (
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]
<em>Substitute equations (ii) and (iii) into equation (i) as follows;</em>
x Q x V = (
x m x v²) - (
x m x u²) -----------------(iv)
<em>Substitute all necessary values into equation (iv) as follows;</em>
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
<em>Solve for Q;</em>
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