Questions in Motion in A Straight Line

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The displacement \[x\] of a particle varies with time \[t,x = a{e^{ - \alpha t}} + b{e^{\beta t}}\], where \[a,\,b,\,\alpha \,{\rm{and }}\beta \]are positive constants. The velocity of the particle will [CBSE PMT 2005]
A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate \[\frac{f}{2}\] to come to rest. If the total distance traversed is 15 S, then
A man is 45 m behind the bus when the bus start accelerating from rest with acceleration 2.5 m/s2. With what minimum velocity should the man start running to catch the bus ?
A particle moves along x-axis as \[x = 4(t - 2) + a{(t - 2)^2}\]. Which of the following is true ?
A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th sec to that covered in 5 sec is
What determines the nature of the path followed by the particle
Two trains, each 50 m long are travelling in opposite direction with velocity 10 m/s and 15 m/s. The time of crossing is
A 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time
A 210 meter long train is moving due North at a of 25m/s. A small bird is flying due South a little above the train with speed 5m/s. The time taken by the bird to cross the train is
A police jeep is chasing with, velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is

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