Applications Of Derivatives Question 208
Question: The equation of motion of a car is $ s=t^{2}-2t $ , where t is measured in hours and s in kilometers. When the distance travelled by the car is $ 15,km $ , the velocity of the car is
Options:
A) $ 2,km/h $
B) $ 4,km/h $
C) $ 2,km/h $
D) $ 8,km/h $
Show Answer
Answer:
Correct Answer: D
Solution:
Given equation $ s=t^{2}-2t $ …..(i) and $ \frac{ds}{dt}= $ velocity $ \frac{ds}{dt}=8\pi r\frac{dr}{dt}=\frac{8\pi \cdot 7.5}{28\pi }=10,cm^{2}/\min $ …..(ii)
Put $ s=15 $ in (i), we get $ t^{2}-2t-15=0 $ or $ (t-5)(t+3)=0 $
$ \therefore t=5 $
Hence velocity of car $ =v=2(5)-2=8,m/s $ .
BETA
