An object is moving along a line with velocity v (t )equals A t squared space plus space B meters per second at time t seconds. Its initial position, at time t equals 0, is s (0 )equals C meters. If A equals 15, B equals 8 and C equals space 3, then Give the object's position function s (t ). Give the distance traveled by the object between t equals 1 and t equals 2 seconds and record your answer below.

- S(t) = 5t³+8t+3

- 19.7m approximately

Explanation:

Given the velocity if an object to be

v(t) = At² + B where t is the time in seconds

Velocity is the change in displacement of a body with respect to time.

V(t) = dS(t)/dt

Making S(t) the subject of the formula

dS(t) = v(t)dt

Integrating both sides

∫dS(t) =∫v(t)dt

S(t) = ∫(At²+B)dt

S(t) = At³/3+Bt + C... 1

In its initial position s(0) = 0

t = 0, s = 0

S(0) = A(0)³/3+B(0)+C

S(0)= C

a) The object's position function s(t) if A = 15, B = 8 and C = 3 can be gotten by substituting this value into eqn 1

S(t) = 15t³/3+8t+3

S(t) = 5t³+8t+3

b) For the distance traveled by the object between t equals 1 and t equals 2 seconds

When t = 1s

S(1) = 5(1)³/3+8(1)+3

S(1) = 5/3+8+3

S(1) = 5+24+9/3

S(1) = 38/3 m

When t = 2secs

S(2) = 5(2)³/3+8(2)+3

S(2) = 40/3+16+3

S(2) = (40+48+9)/3

S(2) = 97/3

Distance travelled between this times will be 97/3-38/3

= 59/3

= 19.7m approximately

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.