Aparticle moves in a straight line so that its velocity at time
tis v(t) = t3. if its position at time t is s(t) and
s(1)= 2, find s(2).

s(2) = 7.75

Step-by-step explanation:

given the velocity v(t) = t^3

we can find the position s(t) by simply integrating v(t) and using the boundary conditions s(1)=2

we know throught s(1) = 2, that at t=1, s =2. we can use this to find the value of the constant c.  

Now we can use this value of t to formulate the position function s(t):

this is the position at time t.

to find the position at t=2

the position of the particle at time, t =2 is s(2) = 7.75

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

theres no picture: /

step-by-step explanation: