1 Given l m is equivalent to 3.28 lf A cube with an edge of 15 ft has a volt eof

Question

1 Given l m is equivalent to 3.28 lf A cube with an edge of 15 ft has a volt eofone 9.6 × 10-2 m 0.21 m 2- A rock is thrown straight up with an initial velocity of 19.6 m/s. What time interval elapses between the rock's being thrown and its return to the original launch point? (Acceleration due to gravity is 9.81 m/s.) B. 5s C. 8s D. 10 s 3- For an object rotating in circular motion with constant speed, doubling the radius means the time (T) and centripetal acceleration (a) will become: A. 2T and 2ac B. Tand a C. ½Tandae D. 2T and as E. ½T and 2a 4- A particle starts from the origin at time r-0 with velocity v, -2 m/s and moves in the x-y plane with a constant acceleration of a- 2 m/s and a,-4 m/s. What will be the - displacement of the particle when its y - displacement becomes 12 m? A. 4m B. 6 m C. 6.8 m D. 8 m E. 12 m 5- The bacterium E coli swims 2 cm west in 14 seconds, remains stationary for 3 seconds, then turns and swins 5 cm at 30° south of west in 40 seconds. Its average speed is: A. 0.123 em/s B. 0.130 cm/s C. 0.119 cm/s D. 0.125 cm/s E. 0.111 cm/s ned by CamScanner

Explanation / Answer

1. given 1m = 3.281 ft

so for a cube of side a = 1.5 ft

volume V = a^3 = (1.5/3.281)^3 = 0.095555 m^3

hence V = 9.6*10^-2 m^3 ( after rounding off)

2. initial velocity, u = 19.6 m/s

time of flight = 2t

where t is time for the ball to reach maximum height

now, u = gt

t = u/g = 19.6/9.81 = 1.997 s

2t = 3.995 s

answer =:> option A : 4s

3. for an object in circular motion withj constant speed u

u = 2*pi*r/t

double the radius

then t becoems double

and centripital acceleration = v^2/r becoems half

option D> 2T and ac/2

4. at t= 0, at origin

vy = 2m/s

ax = 2 m/s/s

ay = 4 m/s/s

at time t

y = 12 m

y = vy*t + 0.5ay*t^2

12 = 2t + 0.5*4*t^2

2t^2 + 2t - 12 = 0

t^2 + t - 6 = 0

solving for t

t = 2 s

hence

x = 0.5*ax*t^2

x = 0.5*2*2^2 = 4 m

hence A. 4 m

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