An object at rest at the origin begins to move in the + x direction with a uniform acceleration of 1   m   s - 2 for 4   s and then it continues moving with a uniform velocity of 4   m   s - 1 in the same direction. The x - t graph for the object's motion will be

Step-by-step solution

The object initially at rest at origin begins to move in the + x direction, thus at x = 0 , u = 0 . Applying the second equation of motion, s = u t + 1 2 a t 2 . Putting the values, we get x = 1 2 a t 2 . Thus, from t = 0 to 4   s , the graph will be parabolic. Now, the object moves with a uniform acceleration a = 1   m   s - 2 for t = 4   s . x = 1 2 × 1 × 4 2 = 8   m . After that, it moves with uniform velocity v = 4   m   s - 1 . We know that v = d x d t = 4 Integrati