Answer:
.
Explanation:
Refer to the velocity-time diagram attached. The displacement of an object over a period of time is equal to the area of the region between the velocity-time plot and the horizontal time axis. That is the case even if the velocity of the object is changing over time.
For the car in this question, the distance travelled in that two seconds should be equal to the trapezoid highlighted in green. That's the region bounded with:
- on the top: the velocity-time function of this car,
- on the two sides: the start and end of the acceleration ( and ,) as well as
- on the bottom: the horizontal time axis.
The formula for the area of a trapezoid is:
.
For the imaginary trapezoid on this velocity-time graph:
- Height: .
- Upper base and lower base: and .
Therefore:
.
Q: A sport car accelerate at the rate of 2.80m/s². How long does it take to reach its top speed of 60.0 km/h, starting from rest ?
Answer:
5.95 s.
Explanation:
From Newton's equation of motion,
a = (v-u)/t ................ Equation 1
Where a = acceleration of the car, v = final velocity of the car, u = initial velocity of the car, t = time taken to reach the top speed.
Making t the subject of the equation,
t = (v-u)/a.............. Equation 2
Given: a = 2.8 m/s², u = 0 m/s ( from rest), v = 60 km/h = (60×1000)/3600
v = 16.67 m/s.
Substitute into equation 2
t = (16.67-0)/2.8
t = 5.95 s.
Hence the time taken to reach the top speed = 5.95 s.