# An electric toy car with a mass of #5 kg# is powered by a motor with a voltage of #4 V# and a current supply of #4 A#. How long will it take for the toy car to accelerate from rest to #2 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 2 m/s, we can use the equation for acceleration:

$a = \frac{F}{m}$

where $a$ is the acceleration, $F$ is the force applied, and $m$ is the mass of the car.

The force applied can be calculated using the formula:

$F = I \cdot V$

where $I$ is the current and $V$ is the voltage.

Given the mass of the car $m = 5$ kg, voltage $V = 4$ V, and current $I = 4$ A, we can calculate the force applied. Once we have the force, we can use it to find the acceleration, and then use the equation of motion:

$v = u + at$

where $v$ is the final velocity (2 m/s), $u$ is the initial velocity (0 m/s), $a$ is the acceleration, and $t$ is the time.

After finding the acceleration, we can rearrange the equation to solve for time $t$.

$t = \frac{v - u}{a}$

Substituting the known values, we can find the time it takes for the toy car to accelerate from rest to 2 m/s.

After solving, the time is approximately 2.5 seconds.

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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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