An electric toy car with a mass of #3 kg# is powered by a motor with a voltage of #7 V# and a current supply of #5 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 #3 kg# is powered by a motor with a voltage of #7 V# and a current supply of #5 A#.  How long will it take for the toy car to accelerate from rest to #2 m/s#?

Amelia Adams · Accepted Answer

The time is #=0.17s#

Voltage is #U=7V#

Current is #I=5A#

The power is

#P=UI=7*5=35W#

Velocity is #v=2ms^-1#

Mass is #m=3kg#

The kinetic energy is

#KE=1/2mv^2=1/2*3*(2)^2=6J#

But,

#E=P*t#

The time is #t=E/P=(6)/35=0.17s#

Amelia 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 formula for acceleration:

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

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

The force $ F $ can be calculated using the formula:

$$ F = I \cdot V $$

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

Then, we can use the formula for acceleration:

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

to find the acceleration.

Next, we can use the formula for uniform acceleration:

$$ v = u + at $$

where:
- $ v $ is the final velocity (2 m/s),
- $ u $ is the initial velocity (0 m/s),
- $ a $ is the acceleration (which we found earlier), and
- $ t $ is the time.

Now, we can rearrange the formula to solve for $ t $:

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

Substitute the known values into the equation and solve for $ t $ to find the time it takes for the toy car to accelerate from rest to 2 m/s.