Question

A particle decelerates uniformly from a speed of 30 cm/s to rest in a time interval of 5.0 s. It then has a uniform acceleration of 10 cm/s2 for another 5.0 s. The particle moves in the same direction along a straight line. The average speed over the whole time interval is?

Answer 1

V=20cm/s

Step-by-step explanation:

The average speed is the distance total divided the time total:

`V=X/T`

First stage:

T1=5s

`v_(f)  =v_(o) - at`

But,
`v_(f)  =0` (decelerates to rest)

then:
`a =v_(o) /t=0.3/5=0.06m/s^(2)`

on the other hand:

`x =v_(o)*t - 1/2*at^(2)=0.3*5-1/2*0.06*5^(2)=0.75m`

X1=75cm

Second stage:

T2=5s

`x =v_(o)*t + 1/2*at^(2)=0+1/2*0.1*5^(2)=1.25m`

X2=125cm

Finally:

X=X1+X2=200cm

T=T1+T2=10s

V=X/T=20cm/s