question_answer 49)

                  A car mass m starts from rest and acquires a velocity along east \[\vec{\upsilon }=v\hat{i}\,\,(\upsilon >\,O)\] in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is                 (a) \[\frac{m\upsilon }{2}\] eastward and is exerted by the car engine.                 (b) \[\frac{m\upsilon }{2}\] eastward and is due to the friction on the typres exerted by the road.                 (c) more than \[\frac{m\upsilon }{2}\] eastward exerted due to the engine and overcomes the friction of the road.                 (d) \[\frac{m\upsilon }{2}\]exerted by the engine.          

Answer:

                  (b) \[\vec{\upsilon }=\,\vec{u}+\,\vec{a}t\,\Rightarrow \,\upsilon \hat{i}\,=0+\,2\vec{a}\]                 \[\therefore \] \[\,\vec{a}\,=\frac{\upsilon }{2}\,\hat{i}\]                 \[\therefore \] \[\vec{F}\,=\,m\vec{a}\,=\,\frac{m\upsilon }{2}\hat{i}\]