4 physics questions?

Question

Hi these are questions from my example placement test for uni. I am not sure of most answers but can you please answer them with an explanation.

1) The length of arc of a circle of radius r = 3 m subtended by the angle θ = 60o. The

length of the arc s is

a. 3 m

b. 180 m

c. 0.05 m

d. 3.14 m

2) The position of a particle moving along the x axis is given by x= (3 + 2t + 1/2t^2)m, with t in seconds. What is the average velocity of the particle between t = 1.0 s and t = 4.0 s?

a. 6.5 m/s

b. 4.5 m/s

c. 12.5 m/s

d. 8.5 m/s

3) A car accelerates from 40 km/h to 75 km/h in 6 seconds. Assuming the acceleration to be

constant, how far does the car travel during this time?

a. 9.6 m

b. 48 m

c. 96 m

d. 190 m

4) A ball is thrown straight up. When the ball reaches the highest point

a. both its velocity and its acceleration are zero.

b. its velocity is zero but its acceleration is not zero.

c. its velocity is not zero but its acceleration is zero.

d. neither its velocity nor its acceleration

Answer 1

1)3.14 m

Explanation:

Circumferences of the circle = 2πr = 18.85 m approx.

The angle of a complete circle is 360 degree, therefore:

360/60 = 6                      -               18.85/6 = 3.14m

2)4.5 m/s

Explanation:

@t= 1.0 s,      x=5.5 m

@t= 4.0 s,     x=19 m

Total distance travelled, S= 13.5

Total time taken, t= 3.0 s

V= 13.5/3 = 4.5 m/s

3)96 m

Explanation:

Vi = 40 km/h x 1,000/3,600 = 11.11 m/s

Vf = 75 km/h x 1,000/3,600 = 20.83 m/s

a = (Vf-Vi)/t = (20.83-11.11)/6 = 1.62 m/s²

S =Vit+1/2at² = (11.11)x6+1/2(1.62)(6)² = 95.82 m

4)b

Explanation:

When the ball reaches the highest point, it stops which implies its velocity is zero but gravitational force/acceleration (9.8m/s²) is still applicable.