A car A is travelling on a straight level roa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the time taken for car $B$ to catch up with car $A$ be $t$ hours.Distance covered by car $A$ in time $t$ is $d_A = 60t$.Distance covered by ca

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(B) Let the time taken for car $B$ to catch up with car $A$ be $t$ hours.Distance covered by car $A$ in time $t$ is $d_A = 60t$.Distance covered by car $B$ in time $t$ with initial velocity $u = 70 	ext{ km/h}$ and deceleration $a = -20 	ext{ km/h}^2$ is $d_B = 70t - \frac{1}{2} 	imes 20 	imes t^2$.Since car $B$ is $2.5 	ext{ km}$ behind car $A$,the condition for catching up is $d_B = d_A + 2.5$.Substituting the expressions: $70t - 10t^2 = 60t + 2.5$.Rearranging the terms: $10t^2 - 10t + 2.5 = 0$.Dividing by $10$: $t^2 - t + 0.25 = 0$.This is a perfect square: $(t - 0.5)^2 = 0$.Therefore,$t = 0.5 	ext{ hours}$.

Similar Questions

$A$ car travelling at $15 \,m/s$ overtakes another car travelling at $10 \,m/s$. Assuming each car is $4 \,m$ long, what is the time taken during the overtake (in $\,s$)?

Explain the concept of relative displacement and its various cases.

$A$ bus is moving with a velocity $10\, ms^{-1}$ on a straight road. $A$ scooterist wishes to overtake the bus in $100\, s$. If the bus is at a distance of $1\, km$ from the scooterist,with what velocity should the scooterist chase the bus? ......... $ms^{-1}$

$A$ ball is dropped from a building of height $45 \, m$. Simultaneously,another ball is thrown up with a speed of $40 \, ms^{-1}$. Calculate the relative speed of the balls as a function of time.

Vedclass Test Series

Exam Paper Generator

Online Exam Module