# An electric toy car with a mass of #1 kg# is powered by a motor with a voltage of #12 V# and a current supply of #4 A#. How long will it take for the toy car to accelerate from rest to #2/5 m/s#?

##### 1 Answer

Aug 18, 2017

#### Explanation:

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

#color(blue)(P=VI)#

- The units of power are
**watts**, where one watt is equivalent to one*joule*(of energy)*per second*. We can use this idea along with the concept of**kinetic energy**to determine the time required to accelerate the toy car to the given velocity.

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

**We have the following information:**

#|->m=1"kg"# #|->V=12"V"# #|->I=4"A"# #|->v=2/5"m"//"s"#

We can calculate power:

#P=(12"V")(4"A)#

#color(blue)(P=48" Joules"//"second")#

Now kinetic energy:

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

#color(blue)(K=2/25"J")#

So, we have:

#2/25cancel("Joules")xx(1"second")/(48cancel(" Joules"))#

#=>1//600" seconds"#

#=>color(blue)(~~0.0017" s")#

Or, in scientific notation,