Question

During the launch of Alan Shepard's Mercury mission (the USA's first human space flight), the Redstone rocket engine fired for 140 seconds. At that time the craft achieved a speed along its trajectory of 2.3 km/s. (a) What is the value of the average acceleration of the craft during that time? (b) Assuming the motion is along a line (we wi later talk about how to deal with the curved path), how far had the craft traveled during that time period? (c) After the engines shut down the capsule separated from the rocket and then was in free flight. If the vertical component of the velocity is 1.63 km/s, how much higher does the capsule go before starting its decent (the gravitational acceleration at that altitude is about 9.45 m/s)? (b. 161 km, c. 140 km) 4 The position of an object as a function of time is given as x = At3 + Bt2 + Ct + D. The constants are A 2.0 m/s, B-1.3 m/s, C4.2 m/s, and D 6 m. (a) What is the velocity of the object at 9.0 s? (b) At what time(s) is the object at rest? (c) What is the acceleration of the object at 0.50 s? (d) Plot the acceleration as a function of time for the time intery に-9.0 s to t = 9.0 s. {a. 505 m/s, b.-1 .08s, 0.65 s c. 8.6 m/s)

Answer 1

The kinematics equations for a uniformally accelerated motion are as follows:

1. $v = u + at$

2. $x = ut + \frac{1}{2}at^{2}$

3. $v^{2}=u^{2} +2ax$

where, v is final velocity

u is initial velocity

t is time interval

x is displacement

a is acceleration