A particle moves along X direction with constant acceleration. it velocity after 4s is 18 m/s and displacement is 56m find out its initial velocity and acceleration?

1 Answer
Jun 10, 2017

Initial velocity: #10"m"/"s"#

Acceleration: #2"m"/("s"^2)#

Explanation:

We're asked to find the initial velocity #v_(0x)# and the acceleration #a_x# of an particle moving in one dimension with a known velocity and position at a certain time.

To find the initial velocity, we can use the equation

#x = x_0 + ((v_x + v_(0x))/2)t#

We'll take the initial position #x_0# to be #0#. Let's rearrange this equation to solve for the initial velocity #v_(0x)#:

#x/t = (v_x + v_(0x))/2#

#v_(0x) = (2x)/t - v_x#

Plugging in known values, we have

#v_(0x) = (2(56"m"))/(4"s") - 18"m"/"s" = color(red)(10"m"/"s"#

The initial velocity is thus #10"m"/"s"#.

#-------------------#

Now that we know the initial velocity, we can use the equation

#v_x = v_(0x) + a_xt#

to find its acceleration. Rearranging the equation to solve for #a_x#, and plugging in known values, we have

#a_x = (v_x - v_(0x))/t = (18"m"/"s" - 10"m"/"s")/(4"s") = color(blue)(2"m"/("s"^2)#

The acceleration of the particle is thus constant at #2"m"/("s"^2)#.