Home /
Expert Answers /
Calculus /
on-the-test-track-a-new-electric-car-model-is-found-to-accelerate-from-rest-along-astraight-path-pa516
(Solved): On the test track, a new electric car model is found to accelerate from rest, along astraight path, ...
On the test track, a new electric car model is found to accelerate from rest, along a
straight path, with an acceleration given by
a(t) = t^1.5(ms^-2)
(Distances are in metres and time, t, is in seconds).
a) What is the velocity of the car at t = 5 seconds?
b) How far is the car from its starting point, at t = 5 seconds?
c) If the mass of the car is 2000 Kg, how much work is done to move the car during the period
from t = 0 seconds tot = 5 seconds?
[Hint: in Part c) you will need to express the distance travelled as a function of t, then use
substitution (i.e. change of integration variable) and force=mass multiplied by acceleration to get
an integral over the time interval].
Question 3: On the test track, a new electric car model is found to accelerate from rest, along a straight path, with an acceleration given by \[ a(t)=t^{1.5}\left(\mathrm{~ms}^{-2}\right) \] (Distances are in metres and time, \( t \), is in seconds). a) What is the velocity of the car at \( t=5 \) seconds? b) How far is the car from its starting point, at \( t=5 \) seconds? c) If the mass of the car is \( 2000 \mathrm{Kg} \), how much work is done to move the car during the period from \( t=0 \) seconds to \( t=5 \) seconds? [Hint: in Part c) you will need to express the distance travelled as a function of \( t \), then use substitution (i.e. change of integration variable) and force=mass multiplied by acceleration to get an integral over the time interval].