An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #15 V# and a current supply of #15 A#. How long will it take for the toy car to accelerate from rest to #5 m/s#?

Question

An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #15 V# and a current supply of #15 A#.  How long will it take for the toy car to accelerate from rest to #5 m/s#?

Charles Aeschliman · Accepted Answer

#0.222 "s"#

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

#P = IV#

#= (15 "V") * (15 "A")#

#= 225 "W"#

The change in kinetic energy for the car is

#Delta "KE" = 1/2 m (v^2 - v_0^2)#

#= 1/2 (4 "kg") ((5 "m/s")^2 - (0 "m/s")^2)#

#= 50 "J"#

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

#t = frac{Delta "KE"}{P}#

#= frac{50 "J"}{225 "W"}#

#= 0.222 "s"#

Btw there should be some kind of error. A toy car wouldn't have that kind of batteries.

Nathan Ashcroft · Answer

undefined To calculate the time it takes for the toy car to accelerate from rest to 5 m/s, we can use the formula:

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

where:
- $ t $ is the time taken to accelerate (in seconds),
- $ m $ is the mass of the car (4 kg),
- $ v $ is the final velocity (5 m/s),
- $ F $ is the net force acting on the car.

First, we need to find the net force acting on the car using the formula:

$$ F = m \cdot a $$

where:
- $ a $ is the acceleration of the car.

Given that the car starts from rest, the initial velocity $ u $ is 0 m/s. Therefore, the acceleration $ a $ can be calculated using the formula:

$$ v^2 = u^2 + 2a \cdot s $$

where:
- $ s $ is the distance traveled by the car (unknown).

Solving for $ a $, we get:

$$ a = \frac{v^2}{2 \cdot s} $$

Since the car starts from rest, the distance traveled $ s $ can be expressed as:

$$ s = \frac{1}{2} \cdot a \cdot t^2 $$

Rearranging the equation to solve for $ t $, we get:

$$ t = \sqrt{\frac{2 \cdot s}{a}} $$

Substituting the expression for $ s $ and the calculated value of $ a $ into the equation, we can find the time $ t $ it takes for the car to accelerate from rest to 5 m/s.