An electric toy car with a mass of #5 kg# is powered by a motor with a voltage of #6 V# and a current supply of #5 A#. How long will it take for the toy car to accelerate from rest to #8 m/s#?

Question

An electric toy car with a mass of #5 kg# is powered by a motor with a voltage of #6 V# and a current supply of #5 A#.  How long will it take for the toy car to accelerate from rest to #8 m/s#?

Emily Abbate · Accepted Answer

The time is #=5.33s# The power is #P=UI=6*5=30W# The energy is #E=1/2mv^2=1/2*5*8^2=160J# But, #E=P*t# #t=E/P=160/30=16/3=5.33s#

Xavier Adame · Answer

undefined To calculate the time it takes for the toy car to accelerate from rest to 8 m/s, we can use the equation:

$$v = u + at$$

Where:
- $v$ is the final velocity (8 m/s)
- $u$ is the initial velocity (0 m/s, since the car starts from rest)
- $a$ is the acceleration (which we need to find)
- $t$ is the time (which we need to find)

Rearranging the equation to solve for $t$:

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

Given that the toy car has a mass of 5 kg, we can use Newton's second law of motion to find the acceleration ($a$):

$$F = ma$$

Where:
- $F$ is the force applied (which we can find using the power supplied to the motor)
- $m$ is the mass (5 kg)
- $a$ is the acceleration

The power ($P$) supplied to the motor can be calculated using the formula:

$$P = VI$$

Where:
- $V$ is the voltage (6 V)
- $I$ is the current supply (5 A)

Using the power ($P$) and the equation $P = Fv$, we can find the force ($F$) applied to the toy car. Then, using $F = ma$, we can find the acceleration ($a$). Finally, substituting the known values into the equation $t = \frac{v - u}{a}$, we can find the time ($t$) it takes for the toy car to accelerate from rest to 8 m/s.