Explanation Formula used: The slope of the velocity-time graph of an object represents the acceleration of the object. Since the slope of the velocity-time graph remains constant, the acceleration will also be constant. Write the expression for the acceleration of the object. a = v f − v i t f − t i ........ (1) Here, a is the acceleration of the object, v i is the initial velocity, v f is the final velocity, t i is the initial time instant and t f is the final time instant. The expression of the speed of the object is obtained by the equation of the line of the velocity-time graph. Write the expression for the velocity of the object. v ( t ) = ( m ⋅ t ) + v i ........ (2) Here, v ( t ) is the speed of the object, m is the slope of the graph i.e. the acceleration and t is the time taken. The expression of the position of the object is obtained by the integration of the expression of velocity of the object. Write the expression for the position of the object. x ( t ) = ∫ v ( t ) ⋅ d t ........ (3) Here, x ( t ) is the position of the object at an instant. Calculation: Substitute 50 m / s for v i , − 50 m / s for v f , 0 s for t i and 10 s for t f in equation (1). a = − 50 m / s − 50 m / s 10 s − 0 s = − 100 10 m / s 2 = − 10 m / s 2 The negative sign shows that the acceleration is in the direction opposite to the motion of the ball

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Chapter 2, Problem 106P

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