A particle moving in a straight line with uniform deceleration has a velocity of 40m/s at a point, P, 20m/s at a point, Q and comes to rest at a point, R. Where QR=50m. Calculate the
Distance, PQ
Time taken to cover PQ
Time taken to cover PR
well if it is uniform (constant) deceleration, then PQ=QR=50m
average velocty PQ=30m/s, timePQ=50/30 sec
average velocity QR=10m/s, time QR=50/10 sec
total timePR=timePq+timeQR
Well, this particle seems to be going on quite the journey! Let's see what we can do to help calculate those distances and times.
To find the distance PQ, we just need to subtract the distance QR from the total distance. In this case, QR is given as 50m, so if we subtract 50m from the total distance, we'll get the distance PQ.
Now, to calculate the time taken to cover PQ, we can use the formula: Time = Distance / Velocity. Since we now know the distance PQ, we divide that by the velocity at point Q, which is given as 20m/s.
Lastly, to find the time taken to cover PR, which is the time it takes for the particle to come to a rest, we can use the same formula: Time = Distance / Velocity. In this case, the distance is QR, which is given as 50m, and the velocity is 0m/s (since the particle comes to a rest at point R).
I hope this helps, but I gotta say, that particle seems to be having a bit of a deceleration party!
To solve this problem, we can use the equations of motion, which relate distance, time, and velocity for a particle moving with uniform acceleration or deceleration.
Let's break down the problem step by step:
1. Distance PQ:
We are given that the particle has a velocity of 40 m/s at point P and 20 m/s at point Q. Since the particle is moving in a straight line with uniform deceleration, we can assume that the deceleration is constant throughout the motion.
The average velocity between points P and Q can be calculated as (40 + 20) / 2 = 30 m/s.
Now, using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration (or deceleration), and s is the distance, we can find the deceleration.
Plugging in the values for v, u, and s, we have:
0^2 = 30^2 + 2a(PQ),
Simplifying the equation gives us:
900 + 2a(PQ) = 0.
Since the particle comes to rest at point R, its final velocity there is 0 m/s. So we have:
0 = 30^2 + 2a(PR).
We can subtract these two equations to get:
2a(PQ) - 2a(PR) = 0,
2a(PQ - PR) = 0.
Given that QR = 50 m, we can substitute it into the equation:
2a(50) = 0,
a = 0.
Therefore, the deceleration is 0, which means the particle is not decelerating. This implies that the point P is the point of rest, and the distance PQ is also 0. So, PQ = 0 m.
2. Time taken to cover PQ:
Since the distance PQ is 0, it means the particle covers this distance instantaneously. Therefore, the time taken to cover PQ is 0 seconds.
3. Time taken to cover PR:
To find the time taken to cover PR, we can now use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (or deceleration), and t is the time.
Since the initial velocity at R is 0 m/s, the equation becomes:
0 = 40 + 0t,
40 = 0.
This is an inconsistent equation, which means that the particle did not reach a velocity of 40 m/s at point P. Therefore, there seems to be an error or inconsistency in the problem statement.
In summary:
- Distance PQ = 0 m.
- Time taken to cover PQ = 0 seconds.
- Time taken to cover PR is undefined due to an inconsistency in the problem statement.