Theory question 107
DynamicsA car travelling at a velocity of 50 km h−1, covers a distance of 20km. If it was accelerating at 6km h−2, calculate, correct to one decimal place, the time the car took to cover the distance.
Show the model answer
Model answer
s = ut + ½at2: 20 = 50t + 3t2
3t2 + 50t − 20 = 0
t = (−50 + √2740)/6 ≈ 0.39
t ≈ 0.4 hours (about 23 minutes)
(Taking 50 km h−1 as the final speed instead also gives 0.4 h.)
Explanation
Use s = ut + ½at² and solve the quadratic in t, keeping the positive root.