Question

The motion of an object along a horizontal hallway is given by ?(m) = 10m + 4 ? ? ∙ t − 2 ? ? 2 ∙ ? 2 . Determine

a. The initial position of the object;

b. The initial velocity of the object;

c. The acceleration of the object?

d. The average velocity of the object from 4 to 10 s.

e. The velocity of the object after 10s

Answer 1

X(t) = 10+4t-2t^2

(a) put t= o sec

X(t) = 10 m answer

(b) differentiate with respect to 't'

V(t) = 4-4t

For initial velocity t= 0

V(0) = 4 m/sec

(c) again differentiate with respect to 't'

a(t) = -4 m/sec^2

a(0) = -4 m/sec^2

(d) average velocity is equal to total displacement upon total time

X(4) = - 6 m

X(10) = -150 m

Total displacement = -150-(-6)

= -144 m

Total time = 6 sec

Average velocity = 144/6 =- 24 m/sec

(e)

V(t) = 4-4t

t= 10 sec

V(10) = 4-4(10)

V(10)= -36 m/sec

X(0) = 10 + 4(0)-2(0)^2

X(0) = 10 m

X(10) = 10 +4×(10)- 2×(10)^2

X(10) =-150 m

Distance = 150 +10

Distance = 160