A particle moves along a straight line and its velocity depends on time as v = 4t - t2. Then for first 5 s:

Average velocity,v=∫05 vdt∫05 dt=∫05 4t−t2dt∫05 dt=2t2−t33055=50−12535=253×5=53 ms-1For average speed, let us put v = 0, which gives t = 0 and t = 4 s∴  Average speed =∫04 vdt+∫45 vdt∫05 dt=∫04 4t−t2dt+∫45 vdt5                                    =2t2−t3304+2t2−t33455                                   =2t2−t3304+2t2−t33455=135ms−1 For acceleration: a=dvdt=ddt4t−t2=4−2t At t=0, a=4 ms−2Therefore, options (3) and (4) are correct, and options (1) and (2) are wrong.