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#?

Question

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#?

Julia Aguilar · Accepted Answer

#0.625 "s"#

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

#P = IV#

#= (4 "V") * (4 "A")#

#= 16 "W"#

The change in kinetic energy for the car is

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

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

#= 10"J"#

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

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

#= frac{10 "J"}{16 "W"}#

#= 0.625 "s"#

Lily Adams · Answer

undefined 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.