A 154 kg bear runs up a hill that has a slope of 15 degrees. The dude travels 1200 m in 125 seconds. A) How much work did the bear do on itself? B.) How much power did the bear develop?

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Ответ:

zeesharpe05

05.07.2020

Physics

t=3.64s

Step by step explanation

Step 1

In this step we use the definition of acceleration to determine the expression to integrate. Note that the acceleration is the derivative of velocity with respect to time.

$a=\frac{dv}{dt} \\\implies adt=dv\\\implies dv=(32t^3-11t^4)dt$

Step 2

Perform integration on the expression from step 1. This calculation is performed as shown below.

$v=\int(32t^3-11t^4)dt\\v=\frac{32}{4}t^4- \frac{11}{5}t^5 +c\\\8t^4- \frac{11}{5}t^5 +c$

Step 3

In this step we use the condition that at t=0 , the velocity v=0 to find the exact form of the velocity function. We substitute this point into the velocity function we found in step 2.

$0=8(0)^4-\frac{11}{5} (0)^5+c\\\implies c=0$

Step 4

We now use the function in step 3 to find out when the velocity is zero again.

$v=0=8t^5-\frac{11}{5}t^4\\\implies 0=8t^4-\frac{11}{5} t^5\\\implies t^4(8-\frac{11}{5} t)\\\implies t=0, 8-\frac{11}{5}t=0\\\\\implies t=0,t=\frac{40}{11} =3.64$

The velocity is zero again when t=3.64

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