A rocket propelled car starts from rest at x = 0 and moves in the positive direction of x with constant acceleration a = 5m/s 2 for 8 seconds until the fuel is exhausted. it then continues with constant velocity. what distance does the car cover in 12 seconds?
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We will be using three formulae here:
(1) S = u + 1/2(vt²) ; where u = initial velocity, v = final velocity and t = time
(2) v² - u² = 2at; where u = initial velocity, v = final velocity, t = time and a = acceleration
(3) Speed = Distance/Time
We are given the following:
a = 5 m/s²
t1 = 8 seconds
Total time = 12 seconds
From formula (1), we have
S1 = ut + 1/2(at²) ----------- please note initial velocity is zero; hence ut = 0
S1 = 0 + 1/2(5 x 8²) = 160 m
From formula (2), we have
v² - u² = 2at
v = √2at = 40 m/s
From formula (3), we have
Speed = Distance/Time or Distance = Speed x Time
Since the time for covering the 1st distance was 8 seconds, the time remaining for the journey will be 12 - 8 = 4 seconds.
Hence Distance S2 = 40 x 4 = 160 m
Total distance can be give as S1 + S2 = 160 + 160 = 320 m
(1) S = u + 1/2(vt²) ; where u = initial velocity, v = final velocity and t = time
(2) v² - u² = 2at; where u = initial velocity, v = final velocity, t = time and a = acceleration
(3) Speed = Distance/Time
We are given the following:
a = 5 m/s²
t1 = 8 seconds
Total time = 12 seconds
From formula (1), we have
S1 = ut + 1/2(at²) ----------- please note initial velocity is zero; hence ut = 0
S1 = 0 + 1/2(5 x 8²) = 160 m
From formula (2), we have
v² - u² = 2at
v = √2at = 40 m/s
From formula (3), we have
Speed = Distance/Time or Distance = Speed x Time
Since the time for covering the 1st distance was 8 seconds, the time remaining for the journey will be 12 - 8 = 4 seconds.
Hence Distance S2 = 40 x 4 = 160 m
Total distance can be give as S1 + S2 = 160 + 160 = 320 m
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