To solve this problem, we can use the equations of motion in kinematics. Here are the equations that will be helpful:
1. v = u + at: This equation relates the final velocity (v) to the initial velocity (u), acceleration (a), and time (t).
2. s = ut + (1/2)at^2: This equation relates the distance traveled (s) to the initial velocity (u), time (t), and acceleration (a).
3. v^2 = u^2 + 2as: This equation relates the final velocity (v) to the initial velocity (u), distance traveled (s), and acceleration (a).
Let's define the variables for this problem:
u1 = initial velocity of the pickup truck (which is 0 m/s since it is stopped)
a1 = acceleration of the pickup truck (5.0 m/s^2)
u2 = initial velocity of the motorcycle (18 m/s)
a2 = acceleration of the motorcycle (0 m/s^2 since it is traveling at a constant speed)
s = distance traveled by the pickup truck before overtaking the motorcycle
t = time taken by the pickup truck to overtake the motorcycle
As the motorcycle is already passing the pickup truck when the light turns green, we can assume that the pickup truck starts from rest. Therefore, using equation 1, we can find the time taken by the pickup truck to reach the same velocity as the motorcycle:
v1 = u1 + a1t
18 = 0 + 5.0t
t = 18/5.0
t = 3.6 seconds
Now we can use equation 2 to find the distance traveled by the pickup truck in this time:
s = u1t + (1/2)a1t^2
s = 0 * 3.6 + (1/2) * 5.0 * (3.6)^2
s = 0 + (1/2) * 5.0 * 12.96
s = 32.4 meters
Therefore, the pickup truck will travel a distance of 32.4 meters before overtaking the motorcycle.
A pickup truck is stopped at a red light. When the light turns green and the pickup just starts to accelerate uniformly at 5.0 m/s2, a motorcycle travelling at a constant 18 m/s passes the pickup in the adjacent lane. How far will the pickup truck travel before it overtakes the motorcycle?
I'd like it if you provide me the equations needed for the problem, it's been years that I've touched any mathematics so this is really confusing to me. (So far I've learned kinematics and velocity-time/position-time graph equations) It's not necessarily time-limited but I just want to understand how it works. Thanks
1 answer