Sketch graphs of velocity and acceleration as a function of time for a car as it strikes a telegraphic pole. Repeat for a billiard ball in a head on collision with the edge of the billiard table.

The velocity of a car as a function of time is shown in Fig. Find the distance travelled by the car in 8 s and its acceleration.

Anwer carefully, with reasons: a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)? Is the total linear momentum conserved during the short time of an elastic collision of two balls? c) What are the answers to a) and b) for an inelastic collision? d) If the potenital energy of two billiard balls depends only on the separation distance between their centers, is the collision elastic or inelastic? (note we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Graphs are very useful to represent a physical situation. Various quantities can be easily represented on graphs and other quantites can be determined from the graph. For example the slope of velocity-time graph represents instantaneous acceleration. For a motion with constant acceleration slope of velocity-time graph is constant. If acceleration is changing with time, slope with change and thus velocity-time graph will be a non-linear curve. Further the area of velocity-time graph gives displacement. A car starts from rest with a constant acceleration a_(1) for some time and attains a velocity v_(0) . Then it immediately retards at a constant rate a_(2) to rest. The total time to journey is t_(0) Identify the correct velocity-time graph

A light rigid rod has a small ball of mass m attached to its one end. The other end is hinged on a table and the rod can rotate freely in vertical plane. The rod is released from vertical position and while falling the ball at its end strikes a hemisphere of mass m lying freely on the table. The collision between the ball and the hemisphere is elastic. The radius of hemisphere and length of the rod are R and 2R respectively. Find the velocity of the hemisphere after collision.

Sita is driving along a staight highway in her car. At time t=0 , when Sita is moving at 10ms^-1 in the positive x-direction, she passes a signpost at x=50m . Here acceleration is a function of time: a=2.0ms^-2-(1/10ms^-3)t a. Derive expressions for her velocity and position as functions of time. b. At what time is her velocity greatest? c. What is the maximum velocity? d. Where is the car when it reaches the maximum velocity?

A ball having mass m and velocity u makes a head on collision with another ball. After collision velocity of the ball of mass m was found to be V in the direction of its original motion. The interaction force between the two balls during their collision has been shown in the graph. The area of the shaded part of the graph is same as the area of the not shaded part. Find the velocity of the balls at the instant they were having equal velocity.

A car starts moving from rest on a horizontal ground such that the position vector of car with respect to its starting point is given as vec(r) = b t hat(i) - c t^(2) hat(j) , where a and b are position constants, direction (x and y axes) intersect at the starting point of car (origin). Find: (a) The equation of the trajectory of car y = f(x) . (b) The angle between direction of velocity and acceleration of car as a function of time theta = f (t) . (c) Average velocity of car over first t seconds of motion