A particle is moving along a straight line with constant acceleration. At the end of tenth second its velocity become 20 m/s and in tenth second it travels a distance of 10 m. Then the acceleration of the particles will be
Question
A particle is moving along a straight line with constant acceleration. At the end of tenth second its velocity become 20 m/s and in tenth second it travels a distance of 10 m. Then the acceleration of the particles will be
Solution
To solve this problem, we need to use the equations of motion.
The equation for velocity after a certain time with constant acceleration is:
v = u + at
where: v = final velocity u = initial velocity a = acceleration t = time
The equation for distance travelled in a certain time with constant acceleration is:
s = ut + 0.5at^2
where: s = distance travelled u = initial velocity a = acceleration t = time
From the problem, we know that at the end of the tenth second, the velocity is 20 m/s. This means that:
20 = u + 10a ---- (equation 1)
We also know that in the tenth second, the particle travels 10 m. This means that the distance travelled in the tenth second is the total distance travelled in 10 seconds minus the total distance travelled in 9 seconds. So:
10 = (u10 + 0.5a10^2) - (u9 + 0.5a9^2) 10 = u + 5a10 - (u + 4.5a9) 10 = 0.5a ---- (equation 2)
Now we can solve these two equations simultaneously. From equation 2, we find that a = 20 m/s^2. Substituting this into equation 1, we find that u = 0 m/s.
So, the acceleration of the particle is 20 m/s^2.
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