A particle move rectilinearly with a constant acceleration of 1m/s2? .its speed after 10second is 5 m/s .The distance cover by particle in this duration is ? (

Question

A particle move rectilinearly with a constant acceleration of 1m/s² .its speed after 10second is 5 m/s .The distance cover by particle in this duration is ? ( intial and final velocities are in opposite direction )

Answer 1

If it started from 0 and accelerated at 1 m/s/s for 10 s how fast would it be going?

=> 10 m/s

So it must have started from a negative speed of -5 m/s to get to 5 m/s after 10 sec.

 

Are you sure it is asking for distance and not displacement?

Start at a point, go for 5 sec negative while slowing to 0 m/s,

   then 5 sec positive speeding up to 5 m/s

And you get back to where you started => displacement is zero.

The distance traveled is from the formula x_f = x₀ + v₀t + 1/2(at²)

but you need to do it in 2 parts

SO

x = 1/2(at²) = 1/2(1 m/s/s) (5 s)²

   = 12.5 m in negative direction

them another 12.5 meters coming back

  = 25 meters distance traveled.