A car starts from rest at a stop sign. It accelerates at 4.0 m/s2 for 6 seconds,

Question

A car starts from rest at a stop sign. It accelerates at 4.0 m/s2 for 6 seconds, coasts for 6 s, and then slows down at a rate of 3.0 m/s2 for the next stop sign. How far apart are the stop signs? (Or, how far does the car travel between stops?)

HINTS: You probably want to break this problem into three separate pieces. And, who knows, you might even want to start by drawing a motion diagram. What is the initial velocity if the car starts from rest? Notice that the "final" velocity after the first acceleration will be the "initial" velocity for the coasting portion. Is "coasting" a case of uniform acceleration? And what does "coasting" mean about the velocity at beginning of the slowing down? (Are these really hints, or just a set of annoying questions??) The answer is NOT 522 m.

Explanation / Answer

Here,

a1 = 4 m/s^2

t1 = 6 s

t2 = 6 s

a2 = 3 m/s^2

time taken to stop , t3 = 4 * 6/3 = 8 s

Now , using second equation of motion

total distance moved = 0.5 * a1 * t1^2 + a1 * t1 * t2 + 0.5 * a2 * t3^2

total distance moved = 0.5 * 4 * 6^2 + 4 * 6 * 6 + 0.5 * 3 * 8^2

total distance moved = 312 m

the total distance moved by car between signs is 312 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.