Question

S) If, in the figure, you start from the Bakery, travel to the Cafe, and then to the Art Gallery (a) what distance you have traveled? 50m b) what is your displacement? -25o Nurth 2.50 km 4.00 km Art Gallery 9) If you run a complete loop around an outdoor track of length 400 m in 100 s, find your (a) average velocity and (b) average speed. 10) A car is traveling north at 17.7 ms. After 12 s its velocity is 14.I m/s in the sime direction. Find the 10 magnitude and direction of the car's average acceleration A) 0.30 m/s2, north C) 2.7 m/s2, north 8) 0.30 m/s2, south D) 2.7 m/s2, south 11) A car with good tires on a dry road can decelerate (slow down) at a steady rate of about 5.0 1) m/s2 when braking. If a car is initially traveling at 53 mi/h (a) how much time does it take the car to stop? (b) what is its stopping distance? 12) An airplane starts from rest and accelerates at a constant 10.8 m/s2. What is its speed at the end of a 1 C) 186 m's 13) To determine the height of a bridge above the water, a person drops a stone and measures the time 1 400 m-long runway? A) 65.7 m/s В) 4320 mis D) 370 m/s E) 93.0 ms it takes for it to hit the water. If the time is 2.3 s, what is the height of the bridge? Neglect air resistance A) 26 m B) 14 m C) 32 m D) 10 m E) 52 m 14) An object is thrown upwards with a speed of 16 m/s. How long does it take it to reach a height of 7.0 m on the way up? Neglect air resistance A) 2.4s B) 3.1s C) 42 s D) 1.2 s E) 0.52 s

I want the best and shortest way to solve them step by step.

Answer 1

8.

(a)

$d=(4.00+4.00+2.50)\:km= 10.50\: km$

(b)

$d=-2.50\: km$

9.

(a)

$v_{avg}=\frac {displacement}{time}=\frac {0}{100}=0$

(b)

$s_{avg}=\frac {distance}{time}=\frac {400}{100}=4\: m/s$

10.

$a=\frac {v-u}{t}=\frac {14.1-17.7}{12}\: m/s^2=-0.3\: m/s^2$

So the magnitude of the acceleration is 0.3 m/s^2 and the negative sign indicates that the direction of the average acceleration is to the south.

11.

(a)

$t=\frac {v-u}{a}=\frac {0-24.6}{(-5.0)}=4.92\: s$

(b)

$s=\frac {v^2-u^2}{2a}=\frac {0-24.6^2}{2\cdot (-5.0)}=60.52\: m$

12.

$v=\sqrt {u^2+2as}=\sqrt {0^2+2\cdot 10.8\cdot 400}\: m/s= 93\: m/s$
13.

$h=\frac {1}{2}gt^2=\frac {1}{2}\cdot 9.8\cdot 2.3^2=26\: m$

14.

$h=ut-\frac {1}{2}gt^2$

$7=16t-0.5\cdot 9.8t^2$

$4.9t^2-16t+7=0$

$t=0.52\: s$