# An electric toy car with a mass of #3 kg# is powered by a motor with a voltage of #8 V# and a current supply of #15 A#. How long will it take for the toy car to accelerate from rest to #7 m/s#?

The power input is the product of the voltage and the current.

The change in kinetic energy for the car is

Thus, the time needed is the energy divided by the power.

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To find the time it takes for the toy car to accelerate from rest to 7 m/s, you can use the formula for acceleration:

[ a = \frac{F}{m} ]

where ( a ) is the acceleration, ( F ) is the force, and ( m ) is the mass.

First, calculate the force acting on the toy car using the formula:

[ F = I \times V ]

where ( I ) is the current and ( V ) is the voltage.

Then, use the formula for acceleration:

[ a = \frac{F}{m} ]

Once you have the acceleration, you can use the formula for acceleration to find the time:

[ v = u + at ]

where ( v ) is the final velocity, ( u ) is the initial velocity (which is 0 m/s since the car starts from rest), ( a ) is the acceleration, and ( t ) is the time.

Rearrange the equation to solve for ( t ):

[ t = \frac{v - u}{a} ]

Substitute the given values and solve for ( t ).

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