Question

Design a three part, 1D, Kinematics problem, Solve it (finding the total time and distance traveled) and show it x(t), v(t), a(t) graph.

make the initial x(t) as zero but the initial v(t) can not be zero. for example, you could start at a constant speed, then slow to a stop, then speed up in the same direction (or go in reverse). Or you could start at certain speed, immediately speed up, then stay at that new speed for (say 200 meters) a while

Answer 1

A body starts at x = 0, at time t = 0. The initial velocity of the body is 10 ms-1. It moves with this velocity for 5 secs and then deacclerates at a rate of 2ms-2 till it finally stops. Find the distance travelled by the body, and the total time taken.

Solution:

In the first 5 secs, motion is uniform and so, distance travelled = velocity * time.

=> distance travelled in first 5 secs = 10 * 5 m = 50m

After t = 5 secs,

Initial velocity of body = 10 ms-1

Final velocity of body = 0 ms-1

Acceleration = -2 ms-2

Since the acceleration is uniform, we can use the formula, v = u + at, where, v is final velocity, u is initial velocity, a is acceleration, and t is time taken.

Substituting the values of v, u & a, we have

0ms-1 = 10ms-1 -2ms-2 * t(s)

=> t (s) = 10 / 2 sec

=> t = 5 secs

Also, distance can be calculated, using the formula, s = (v + u) * t /2

Substituting the values, we get,

s =( 0ms-1 + 10ms-1) * 5s /2

=> s = 50 /2 m

=> s = 25 m.

Hence, total time taken = 5sec + 5sec = 10 sec

Total distance treavelled = 50m + 25 m = 75m

x(t):

v(t):

a(t):