# An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #7 V# and a current supply of #9 A#. How long will it take for the toy car to accelerate from rest to #7/2 m/s#?

The product of voltage and current is the power input.

The vehicle's change in kinetic energy is

The energy divided by the power equals the amount of time required.

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To find the time it takes for the toy car to accelerate from rest to ( \frac{7}{2} ) m/s, we can use the equation for acceleration:

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

Where:

- ( a ) is the acceleration
- ( F ) is the force
- ( m ) is the mass

We can find the force using the formula for electric power:

[ P = VI ]

Where:

- ( P ) is the power (in watts)
- ( V ) is the voltage (in volts)
- ( I ) is the current (in amperes)

Given that the toy car is accelerating, the force produced by the motor is equal to the product of the current and the voltage:

[ F = VI ]

Now, we can rearrange the equation for acceleration to solve for time:

[ t = \frac{v_f - v_i}{a} ]

Where:

- ( t ) is the time
- ( v_f ) is the final velocity
- ( v_i ) is the initial velocity (0 m/s, as the car starts from rest)
- ( a ) is the acceleration

Given that the final velocity is ( \frac{7}{2} ) m/s, and the initial velocity is 0 m/s, we can substitute these values along with the acceleration found from the force equation into the time equation to find the time it takes for the toy car to accelerate:

[ t = \frac{\frac{7}{2} - 0}{\frac{VI}{m}} ]

[ t = \frac{\frac{7}{2}}{\frac{VI}{m}} ]

[ t = \frac{7m}{2VI} ]

Substitute the given values:

[ t = \frac{7 \times 4}{2 \times 7 \times 9} ]

[ t = \frac{28}{126} ]

[ t \approx 0.222 , \text{seconds} ]

So, it will take approximately 0.222 seconds for the toy car to accelerate from rest to ( \frac{7}{2} ) m/s.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- If a current of #4 A# passing through a circuit generates #96 W# of power, what is the resistance of the circuit?
- If a current of #8 A# passing through a circuit generates #16 W# of power, what is the resistance of the circuit?

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