At launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h; at the end of the first 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in m/s2) of the rocket (i) during the first 8.00 s and (ii) between 8.00 s and the end of the first 1.00 min? (b) Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel (i) during the first 8.00 s and (ii) during the interval from 8.00 s to 1.00 min?
Solution 29E Step 1: Given data Mass of the rocket (m) = 4.5 million pounds When time t = 8 s , speed v = 161 km/h t = 1 minute or 60 s , v = 1610 km/h To find average acceleration in m/s 2 Step 2: (i) t= 8s Acceleration (a) = velocity/time = v/t = 161/8 Acceleration (a) = 20.125 m/s 2 Step 3: (ii) Acceleration between time interval 8s and 1 minute t1 = 8s t2 = 1 min or 60s Speed increases from 161 km/h to 1610 km/h Since the value of acceleration takes unit m/s , units must be changed from km/h to m/s 1000 v 1 = 161 km/p = 161* 60*60 = 44.7222 m/s v 2 = 1610 km/p = 1610* 1000 = 447.222 m/s 60*60