An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #8 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 #8 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#?

William Audy · Accepted Answer

#t~~0.42"s"#

Power can be expressed in terms of current and voltage as:

#color(blue)(P=VI)#

#color(blue)(K=1/2mv^2)#

#=>#where #m# is the object's mass and #v# is its velocity.

We have the following information:

We can calculate power:

#P=(8"V")(15"A)#

#color(blue)(P=120" Joules"//"second")#

Now kinetic energy:

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

#color(blue)(K=50"J")#

So, we have:

#50cancel("Joules")xx(1"second")/(120cancel(" Joules"))#

#=>5/12" seconds"#

#=>color(blue)(~~0.42" s")#

Charlotte Aaron · Answer

undefined It will take approximately 13.3 seconds for the toy car to accelerate from rest to 5 m/s.

Benjamin Asiedu · Answer

undefined To determine the time it takes for the toy car to accelerate from rest to a velocity of $ 5 \, \text{m/s} $, you can use the equation:

$$ v = u + at $$

Where:
- $ v $ is the final velocity ($ 5 \, \text{m/s} $),
- $ u $ is the initial velocity (which is $ 0 \, \text{m/s} $ as it starts from rest),
- $ a $ is the acceleration (which can be calculated using Newton's second law: $ F = ma $, where $ F $ is the force and $ m $ is the mass of the car),
- $ t $ is the time taken.

First, calculate the force ($ F $) exerted on the car using the formula $ F = VI $, where $ V $ is the voltage and $ I $ is the current.

$$ F = (8 \, \text{V})(15 \, \text{A}) $$

Once you have $ F $, use Newton's second law to find the acceleration ($ a $):

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

Now, you have $ a $ and $ v $. Plug these values into the equation $ v = u + at $ and solve for $ t $.