Question

From the same place, two bodies move at the same time in the same direction, body A from rest with acceleration 0.2, body B with initial velocity (Vo) 9 and deceleration 0.1. Calculate:

a) when will the bodies meet again? time?(t)
b) how far will they go until they meet? (s)
c) how many speeds will they have at the meeting place?

Answer 1

To determine when two bodies will meet when moving in the same direction, we equate their displacement equations and solve for time and displacement, then use the velocity formula to find their speeds at the meeting point.

Step-by-step explanation:

To find out when and where two bodies moving in the same direction will meet, we need to set their displacement equations equal to each other and solve for time (t) and displacement (s). We'll use the following kinematic equations for constant acceleration:

• For body A (starting from rest): s = ut + ½(at²) where u=0, a=0.2 m/s²
• For body B (starting with initial velocity): s = ut + ½(-a)t² where u=9 m/s, a=0.1 m/s²

Since body A starts from rest, its initial velocity (u) is 0. For body B, we have an initial velocity (u) of 9 m/s but it's decelerating, so we use a negative acceleration.

(a) To calculate the time when the bodies meet again, we equate their displacement equations:

0 + ½(0.2)t² = 9t + ½(-0.1)t²

Solving the quadratic equation, we can find the value of t.

(b) After finding the t, we plug it back into either of the displacement equations to find s, the distance covered.

(c) To find the velocities at the meeting point, we can use the velocity equation v = u + at for each body, where tis the time calculated.