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 #18 A#. How long will it take for the toy car to accelerate from rest to #7 m/s#?

Question

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 #18 A#.  How long will it take for the toy car to accelerate from rest to #7 m/s#?

Charlotte Aaron · Accepted Answer

The time is #=0.51s#

The power is

#P=UI#

#"Power"="Voltage"xx"Current"#

The voltage is #U=8V#

The current is #I=18A#

The power is

#P=UI=8xx18=144W#

The kinetic energy of the car is

#E=1/2mv^2#

The mass of the car is #m=3kg#

The speed is #v=7ms^-1#

So,

The kinetic energy is

#E=1/2mv^2=1/2xx3xx(7)^2=73.5J#

Let the time #=(t)s#

#E=Pt#

#"Energy=Power" xx "time"#

The time is

#t=E/P=(73.5)/144=0.51s#

Isabella Alvarez · Answer

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

$$ t = \frac{m \cdot v}{F} $$

where:
- $ t $ is the time
- $ m $ is the mass of the toy car (3 kg)
- $ v $ is the final velocity (7 m/s)
- $ F $ is the net force acting on the car

To calculate the net force ($ F $), you can use the equation:

$$ F = I \cdot V $$

where:
- $ I $ is the current supply (18 A)
- $ V $ is the voltage (8 V)

Once you have $ F $, you can substitute it into the first equation to find $ t $.