JEE Main202117 Mar 2021Morning ShiftPhysicsMotion in One DimensionActual
A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance travelled is:
Options
- A4 α β ( α + β ) t 2
- B2 α β ( α + β ) t 2
- Cα β 2 ( α + β ) t 2
- Dα β 4 ( α + β ) t 2
Correct answer
C. α β 2 ( α + β ) t 2
Step-by-step solution
v 0 = α t 1 and 0 = v 0 - β t 2 ⇒ v 0 = β t 2 t 1 + t 2 = t v 0 1 α + 1 β = t ⇒ v 0 = α β t α + β Distance = area of v - t graph = 1 2 × t × v 0 = 1 2 × t × α β t α + β = α β t 2 2 ( α + β )